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Z Score is (x-mu)/sigma. The Z-Score allows you to go to a standard normal distribution chart and to determine probabilities or numerical values.
Go back to the basic data, estimate the sample mean and the standard error and use these to estimate the Z-score.
A z-score is a means to compare rank from 2 different sets of data by converting the individual scores into a standard z-score. The formula to convert a value, X, to a z-score compute the following: find the difference of X and the mean of the date, then divide the result by the standard deviation of the data.
Prob (-1.31 < z < 0.31) = 0.5266
z score = (test score - mean score)/SD z score = (87-81.1)/11.06z score = 5.9/11.06z score = .533You can use a z-score chart to calculate the probability from there.